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Asymptotic normality of nonparametric estimators under [alpha]-mixing condition

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  • Liebscher, Eckhard

Abstract

In this paper we derive central limit theorems for three types of nonparametric estimators: kernel density estimators, Hermite series estimators and regression estimators. We assume that the sample is a part of a stationary sequence satisfying an [alpha]-mixing property. The proofs are based on a central limit theorem for [alpha]-mixing triangular arrays in the paper by Liebscher [1996, Stochastics and Stochastics Rep. 59, 241-258].

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  • Liebscher, Eckhard, 1999. "Asymptotic normality of nonparametric estimators under [alpha]-mixing condition," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 243-250, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:3:p:243-250
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    1. George Roussas, 1969. "Nonparametric estimation in Markov processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 73-87, December.
    2. E. Liebscher, 1990. "Hermite series estimators for probability densities," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 37(1), pages 321-343, December.
    3. Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
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    6. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
    7. P. M. Robinson, 1983. "Nonparametric Estimators For Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(3), pages 185-207, May.
    8. Wu, J. S. & Chu, C. K., 1994. "Nonparametric estimation of a regression function with dependent observations," Stochastic Processes and their Applications, Elsevier, vol. 50(1), pages 149-160, March.
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    Cited by:

    1. Takada, Teruko, 2009. "Simulated minimum Hellinger distance estimation of stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2390-2403, April.
    2. Longla, Martial & Peligrad, Magda & Sang, Hailin, 2015. "On kernel estimators of density for reversible Markov chains," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 149-157.
    3. Jing Wang, 2012. "Modelling time trend via spline confidence band," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(2), pages 275-301, April.

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